The use of # for a suite or apartment number is much older than the 12-button telephone keypad. Its placement, however, is not as shown in the OP. With us, the house or building number precedes the street name but the apartment follows. The slash/virgule is not used at all. Example: 72 President St #4
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Andrew LazarusJun 21 '13 at 22:44

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Carlo, it is used in addresses not because it is associated with addresses but is associated with numbers, and it turns out that apartments are labeled with numbers, that's all. Numbers came before apartments. See the wiki article on the number sign, which accords with my understanding. The wiktionary entry is speculative and deficient.
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MitchJun 22 '13 at 16:24

1 Answer
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This sign is more usually called the pound sign, hash or number sign. According to some theories, the "pound sign" stemmed from a simplification of the abbreviation of lb to mean "pound":

Historically, the pound name derives from a series of abbreviations for pound, the unit of weight. At first "lb." was used; however, printers later designed a font containing a special symbol of an "lb" with a line through the verticals so that the lowercase letter "l" would not be mistaken for the numeral "1"....

Ultimately, the symbol was reduced for clarity as an overlay of two horizontal strokes "=" across two forward-slash-like strokes "//".

So according to this, the hash sign which came to mean "number" (as in, "a #2 pencil" would be spoken as "a number 2 pencil") developed separately from the use of a hash sign in cartography. Similarly, in reference to apartments, the use of a hash sign is simply shorthand. Thus, "apartment number 4" could be written as "apartment #4".